GRE Math : Algebra

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Example Questions

Example Question #381 : Algebra

When the integer is increased by , the result is less than times the integer . What is s-3b ?

Possible Answers:

$\frac{1}{3}$

Correct answer:

Explanation:

The trick for this problem is to translate "When the integer is increased by , the result is less than times the integer ." into mathematical terms. Let's do it piece by piece:

When the integer :

When the integer is increased by :

s+2

When the integer is increased by , the result is:

s+2=

When the integer is increased by , the result is less than:

s+2=-7

When the integer is increased by , the result is less than times the integer :

s+2=3b-7

Now that we have this, solve for

s=3b-9

Now plug this value in for the problem question:

s-3b=(3b-9)-3b=-9

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Example Question #61 : Evaluating Expressions

When the integer is mulitplied by , the result is greater than the product of and the integer . What is 2r-s ?

Possible Answers:

$-\frac{7}{5}$

$\frac{5}{7}$

$\frac{7}{5}$

$-\frac{5}{7}$

Correct answer:

$-\frac{7}{5}$

Explanation:

To solve this problem, translate "When the integer is mulitplied by , the result is greater than the product of and the integer " into mathematical terms. Step-by-step it is:

When the integer :

When the integer is mulitplied by :

When the integer is mulitplied by , the result is:

5s=

When the integer is mulitplied by , the result is greater than:

5s=7+ When the integer is mulitplied by , the result is greater than the product:

5s=7+ *

When the integer is mulitplied by , the result is greater than the product of and the integer :

5s=7+10*r=7+10r

Now, solve for

$s=\frac{7+10r}{5}=\frac{7}{5}+2r$

Now, plug this value into the problem question:

$2r-s=2r-(\frac{7}{5}+2r)=-\frac{7}{5}$

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Example Question #381 : Algebra

For any integer , let x@=x+2

Quantity A: $\frac{16@}{4@}$

Quantity B: $(\frac{16}{4})@$

Possible Answers:

Quantity B is greater.

The two quantities are equal.

Quantity A is greater.

The relationship cannot be determined.

Correct answer:

Quantity B is greater.

Explanation:

Follow the condition given, namely x@=x+2 to evaluate each quantity:

Quantity A:

$\frac{16@}{4@}=\frac{16+2}{4+2}=\frac{18}{6}=3$

Quantity B:

$(\frac{16}{4})@=4@=4+2=6$

Quantity B is greater.

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Example Question #382 : Gre Quantitative Reasoning

For any positive integer , $x@=\frac{x+6}{x}$

Quantity A: $\frac{6@}{3@}$

Quantity B: $(\frac{6}{3})@$

Possible Answers:

The two quantities are equal.

Quantity A is greater.

Quantity B is greater.

The relationship cannot be determined.

Correct answer:

Quantity B is greater.

Explanation:

To solve this problem, follow the operation given for each quantity:

, $x@=\frac{x+6}{x}$

Quantity A:

$\frac{6@}{3@}=\frac{\frac{6+6}{6}}{\frac{3+6}{3}}=\frac{2}{3}$

Quantity B:

$(\frac{6}{3})@=2@=\frac{2+6}{2}=4$

Quantity B is greater.

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Example Question #65 : How To Evaluate Algebraic Expressions

For any positive integer , $x@=\frac{x}{2}$

Quantity A: $\frac{12@}{2@}$

Quantity B: $(\frac{12}{2})@$

Possible Answers:

The two quantities are equal.

Quantity B is greater.

The relationship cannot be determined.

Quantity A is greater.

Correct answer:

Quantity A is greater.

Explanation:

To perform this problem, simply perform the operation , $x@=\frac{x}{2}$ for each quantity:

Quantity A:

$\frac{12@}{2@}=\frac{\frac{12}{2}}{\frac{2}{2}}=\frac{6}{1}=6$

Quantity B:

$(\frac{12}{2})@=6@=\frac{6}{2}=3$

Quantity A is greater.

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Example Question #382 : Algebra

For any integer $x\neq 3$ , x@=x-3

Quantity A: $\frac{4@}{2@}$

Quantity B: $(\frac{4}{2})@$

Possible Answers:

The relationship cannot be determined.

The two quantities are equal.

Quantity A is greater.

Quantity B is greater.

Correct answer:

The two quantities are equal.

Explanation:

To solve this problem, evaluate each quantity using the property x@=x-3 :

Quantity A:

$\frac{4@}{2@}=\frac{4-3}{2-3}=\frac{1}{-1}=-1$

Quantity B:

$(\frac{4}{2})@=2@=2-3=-1$

The two quantities are equal.

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Example Question #65 : Evaluating Expressions

A counselor found that in a group of 240 students, were taking a foreign language, 190 were taking math, and were taking neither. How many students were taking both?

Possible Answers:

110

Correct answer:

Explanation:

For group problems, we may use the group equation:

T=G_1+G_2-B+N

T:Total

G_1:Group_1

G:Group_2

B:Both

N:Neither

Our unknown value is the number of students in both groups:

240=90+190-B+30

240=310-B

-70=-B

B=70

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Example Question #66 : Evaluating Expressions

In a group of 140 employees, can use the cash register, 100 can use the price gun, and can use both. How many employees cannot use either?

Possible Answers:

Correct answer:

Explanation:

For group problems, we may use the group equation:

T=G_1+G_2-B+N

T:Total

G_1:Group_1

G:Group_2

B:Both

N:Neither

140=80+100-60+N

140=120+N

N=20

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Example Question #67 : How To Evaluate Algebraic Expressions

In a group of 225 artists, 115 are able to use traditional media, can use both traditional and digital media, and cannot use either (they work with novel and untraditional methods.) How many artists can only use digital media?

Possible Answers:

110

150

130

Correct answer:

130

Explanation:

For group problems, we may use the group equation:

T=G_1+G_2-B+N

T:Total

G_1:Group_1

G:Group_2

B:Both

N:Neither

225=115+G_2-30+10

225=95+G_2

G_2=130

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Example Question #68 : How To Evaluate Algebraic Expressions

In a group of 330 high school athletes, 200 can play baseball, 195 can play soccer, and can play neither (playing American football instead). How many athletes can play both baseball and soccer?

Possible Answers:

115

Correct answer:

115

Explanation:

For group problems, we may use the group equation:

T=G_1+G_2-B+N

T:Total

G_1:Group_1

G:Group_2

B:Both

N:Neither

330=200+195-B+50

330=445-B

-115=-B

B=115

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GRE Math : Algebra

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #381 : Algebra

Example Question #61 : Evaluating Expressions

Example Question #381 : Algebra

Example Question #382 : Gre Quantitative Reasoning

Example Question #65 : How To Evaluate Algebraic Expressions

Example Question #382 : Algebra

Example Question #65 : Evaluating Expressions

Example Question #66 : Evaluating Expressions

Example Question #67 : How To Evaluate Algebraic Expressions

Example Question #68 : How To Evaluate Algebraic Expressions

All GRE Math Resources

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